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Long hitting time, slow decay of correlations and arithmetical properties
$C^1$ -stably weakly shadowing homoclinic classes admit dominated splittings
1. | LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 |
2. | Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505 |
3. | School of Mathematic Sciences, Peking University, Beijing, 100871 |
[1] |
Flavio Abdenur, Lorenzo J. Díaz. Pseudo-orbit shadowing in the $C^1$ topology. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 223-245. doi: 10.3934/dcds.2007.17.223 |
[2] |
Zhiping Li, Yunhua Zhou. Quasi-shadowing for partially hyperbolic flows. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2089-2103. doi: 10.3934/dcds.2020107 |
[3] |
Wenxiang Sun, Yun Yang. Hyperbolic periodic points for chain hyperbolic homoclinic classes. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3911-3925. doi: 10.3934/dcds.2016.36.3911 |
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S. Yu. Pilyugin, A. A. Rodionova, Kazuhiro Sakai. Orbital and weak shadowing properties. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 287-308. doi: 10.3934/dcds.2003.9.287 |
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Rafael O. Ruggiero. Shadowing of geodesics, weak stability of the geodesic flow and global hyperbolic geometry. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 365-383. doi: 10.3934/dcds.2006.14.365 |
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Zheng Yin, Ercai Chen. The conditional variational principle for maps with the pseudo-orbit tracing property. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 463-481. doi: 10.3934/dcds.2019019 |
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Xiao Wen, Lan Wen. No-shadowing for singular hyperbolic sets with a singularity. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 6043-6059. doi: 10.3934/dcds.2020258 |
[8] |
Sergei Yu. Pilyugin. Variational shadowing. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 733-737. doi: 10.3934/dcdsb.2010.14.733 |
[9] |
S. Yu. Pilyugin, Kazuhiro Sakai, O. A. Tarakanov. Transversality properties and $C^1$-open sets of diffeomorphisms with weak shadowing. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 871-882. doi: 10.3934/dcds.2006.16.871 |
[10] |
Jihoon Lee, Ngocthach Nguyen. Flows with the weak two-sided limit shadowing property. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4375-4395. doi: 10.3934/dcds.2021040 |
[11] |
Amadeu Delshams, Marian Gidea, Pablo Roldán. Transition map and shadowing lemma for normally hyperbolic invariant manifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1089-1112. doi: 10.3934/dcds.2013.33.1089 |
[12] |
Keonhee Lee, Kazuhiro Sakai. Various shadowing properties and their equivalence. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 533-540. doi: 10.3934/dcds.2005.13.533 |
[13] |
Will Brian, Jonathan Meddaugh, Brian Raines. Shadowing is generic on dendrites. Discrete and Continuous Dynamical Systems - S, 2019, 12 (8) : 2211-2220. doi: 10.3934/dcdss.2019142 |
[14] |
Shaobo Gan. A generalized shadowing lemma. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 627-632. doi: 10.3934/dcds.2002.8.627 |
[15] |
Sergey V. Bolotin. Shadowing chains of collision orbits. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 235-260. doi: 10.3934/dcds.2006.14.235 |
[16] |
Sergey Kryzhevich, Sergey Tikhomirov. Partial hyperbolicity and central shadowing. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2901-2909. doi: 10.3934/dcds.2013.33.2901 |
[17] |
S. Yu. Pilyugin. Inverse shadowing by continuous methods. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 29-38. doi: 10.3934/dcds.2002.8.29 |
[18] |
Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355 |
[19] |
Jifeng Chu, Zhaosheng Feng, Ming Li. Periodic shadowing of vector fields. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3623-3638. doi: 10.3934/dcds.2016.36.3623 |
[20] |
Hiromichi Nakayama, Takeo Noda. Minimal sets and chain recurrent sets of projective flows induced from minimal flows on $3$-manifolds. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 629-638. doi: 10.3934/dcds.2005.12.629 |
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